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geom3d

 reflection
 find the reflection of a geometric object in a point, in a line, or in a plane

 Calling Sequence reflection(Q, P, c)

Parameters

 Q - the name of the object to be created P - geometric object c - point, line, or plane

Description

 • In reflection in a point, each point P of the set S of all points of unextended space is carried into the point P1 of S such that PP1 is bisected by a fixed point O of space.
 • In reflection in a line, each point P of S is carried into the point P1 of S such that PP1 is perpendicularly bisected by a fixed line l of space.
 • In reflection in a plane, each point P of S is carried into the point P1 of S such that PP1 is perpendicularly bisected by a fixed plane p of space.
 • For a detailed description of the object created Q, use the routine detail (i.e., detail(Q))
 • The command with(geom3d,reflection) allows the use of the abbreviated form of this command.

Examples

 > $\mathrm{with}\left(\mathrm{geom3d}\right):$

Define the plane oxy.

 > $\mathrm{plane}\left(\mathrm{oxy},\left[\mathrm{point}\left(C,0,0,0\right),\mathrm{point}\left(X,1,0,0\right),\mathrm{point}\left(Y,0,1,0\right)\right]\right):$

Define the sphere with center (1,1,1) and radius 2.

 > $\mathrm{sphere}\left(s,\left[\mathrm{point}\left(o,1,1,1\right),2\right]\right)$
 ${s}$ (1)

Find the reflection of the sphere s in the plane oxy.

 > $\mathrm{reflection}\left(\mathrm{s1},s,\mathrm{oxy}\right)$
 ${\mathrm{s1}}$ (2)
 > $\mathrm{detail}\left(\mathrm{s1}\right)$
 Warning, assume that the name of the axes are _x, _y and _z
 $\begin{array}{ll}{\text{name of the object}}& {\mathrm{s1}}\\ {\text{form of the object}}& {\mathrm{sphere3d}}\\ {\text{name of the center}}& {\mathrm{center_s1_1}}\\ {\text{coordinates of the center}}& \left[{1}{,}{1}{,}{-1}\right]\\ {\text{radius of the sphere}}& {2}\\ {\text{surface area of the sphere}}& {16}{}{\mathrm{\pi }}\\ {\text{volume of the sphere}}& \frac{{32}{}{\mathrm{\pi }}}{{3}}\\ {\text{equation of the sphere}}& {{\mathrm{_x}}}^{{2}}{+}{{\mathrm{_y}}}^{{2}}{+}{{\mathrm{_z}}}^{{2}}{-}{2}{}{\mathrm{_x}}{-}{2}{}{\mathrm{_y}}{+}{2}{}{\mathrm{_z}}{-}{1}{=}{0}\end{array}$ (3)

Check that s and s2, the reflection of s1, are the same.

 > $\mathrm{reflection}\left(\mathrm{s2},\mathrm{s1},\mathrm{oxy}\right)$
 ${\mathrm{s2}}$ (4)
 > $\mathrm{AreDistinct}\left(s,\mathrm{s2}\right)$
 ${\mathrm{false}}$ (5)

Plot the sphere, its reflection and the plane.

 > $\mathrm{draw}\left(\left[s,\mathrm{s1},\mathrm{oxy}\right],\mathrm{style}=\mathrm{patch},\mathrm{lightmodel}=\mathrm{light4}\right)$